How can I lock the screen while at the same time continue to show the active desktop? I want the screen to be protected, but I don't want a screen saver to be shown. Is that possible with KDE? Or another application?

In System Settings -> Display and Monitor -> Screen Locker, you can select between options including Simple Locker (just a background and password prompt), Desktop Widgets (adds the ability to show a limited set of widgets on the locker like a clock, a widget for leaving notes, etc. and Screen saver (Simple Locker with screen saver on top)